Cylinder Wake calculation
I am working on a dissertation project which aims to reduce the vibration of wind turbine structures by pitching the rotor blades, changing the thrust force.
At the moment I am trying to make a model of the flow field downwind of the cylindrical tower from which I can determine the local angle of attack on the rotor blades.
I was not expecting the flow behind a 2-D cylinder to be as complex as it appears to be from my searches for academic papers on the topic.
As a guide, the reynold's number's I am interested in are the order of 10^5. The academic papers I have found say that 3D instabilities occur at around Re=200, and don't say if any other effects come into play at higher Re's.
I understand that this flow is dynamic, although I have a book on wind turbines that says the time-averaged tower wake is sufficient for this application.
I thought about taking the drag coefficient at a particular reynold's number and reversing the wake traverse technique to find the local velocities, assuming the wake has a "1-cos^2" profile, but this is impossible without knowing either the wake width or the peak velocity defecit.
All the material I have found on the flow behind a cylinder uses the Navier stokes equations, which I understand, but then the papers tend to skip the process used to calculate the data before they show those pretty chloropleth pictures of vorticity.
I would like to be able to cretae these vorticity diagrams myself in matlab, because the blade pitch control loop can then be integrated with simulink.
If anybody knows of a report or website explaining how to calculate the wake profile downsream of a cylinder, or even the name of a particular method which I may ot of heard of before, I really would be in your debt. If there is a method for finding the time averaged wake directly then that would be even better.
Thanks for any help which can be offered,
Re: Cylinder Wake calculation
>If anybody knows of a report or website explaining how to calculate the wake profile downsream of a cylinder
You must have some understanding of the acronym "CFD", otherwise you wouldn't post on this forum. Well, then you probably know that the unsteady flow field behind a cylinder at such high Reynolds numbers can only be obtained experimentally or by numerical solution of the unsteady Navier-Stokes equations (Reynolds-averaged NS with an adequate turbulence model should be enough for your purposes). Once you have the unsteady flow field you can obtain a time-averaged wake profile... but I doubt this is what you need for your project.
What you need to know is the unsteady pressure on the surface of your structure. With more or less periodic flow, you'll essentially need the oscillation frequency and pressure amplitude distribution over the surface. This is what's causing the vibration, and you need to find out how to counter-act this unsteady forcing by pitching the blades. This cannot be done by just looking at a time-average flow solution, and certainly not by just looking at the time-average wake profile. Vortex-Induced Vibration (VIV) is caused by unsteady(!) vortex shedding.
>I have a book on wind turbines that says the time-averaged tower wake is sufficient for this application
it's time to buy a new book, maybe one on "structural dynamics of wind turbines", not "statics" :)
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